Sample Medium Term Plans for Maths Using Impact Maths

Sample Medium Term Plans for Maths Using Impact Maths

Key Stage 3

Sample medium term plans for maths using Impact Maths

Year 8

Contents

Planning with the Framework 1

Year 7 planning chart 2

Autumn term 3

Number/algebra 1 3

Shape, space and measures 1 4

Handling data 1 5

Number 2 6

Algebra 2 7

Shape, space and measures 2 8

Spring term 10

Algebra 3 10

Number 3 11

Shape, space and measures 3 12

Algebra 4 13

Handling data 2 14

Summer term 16

Number 4 16

Algebra 5 17

Solving problems 19

Shape, space and measures 4 20

Handling data 3 21

Working with the Impact guide

The Impact maths KS3 scheme has been used in schools since 1998. It has been continually updated to meet the requirements of the Framework for Teaching Mathematics. This document provides a detailed guide of how to deliver the framework using Impact materials.

Heinemann Educational has the permission of the DfES to reproduce their objectives in this matching guide. We have retained all the elements of the DfES sample plans to make it very easy for you to plan your schemes of work for Year 8 using Impact.

For example:

  • Core objectives are in bold as in the medium-term plans.
  • We have given references to the sections in 2G, 2B and 2R.
  • For ease of reference, the layout is very similar to the DfES sample medium-term plans, with the Impact sections in the column(s) alongside.
  • We have repeated the DfES’s columns of ‘support’, ‘core’ and ‘extension’ to help with differentiation across sets.
  • We have also retained the dependencies between topics as the DfES sample plans.

How to use this document

This is a reproduction of the sample medium-term plans produced by the National Numeracy Strategy, reproduced with permission and acknowledgement to the DfES.

Details of how these charts can be used for planning are given on p1. In addition to the material provided by the NNS, detailed cross-references in the teaching objectives for the main activities refer to the Impact maths student books and pupil performance packs. The cross-references in the teaching objectives for the oral and mental activities refer to the lesson starters in the 1R pupil performance pack. There is also a short narrative for each topic of work, giving advice on using Impact and other resources.

All cross-references refer to material in 1G and 1R. Not all of the extension objectives are covered in Impact 1R, and you may need to use resources from higher years to provide extension material.

A matching guide for Year 7 is now available, and Year 9 will be available in the spring term.

Notes on tables

(in pt)section covers point in part.

(pt)part of section covers point.

About the author

Derek Huby is an experienced primary and secondary numeracy consultant, as well as being an experienced maths teacher and head of department.

Acknowledgement

We would like to thank Derek Huby and Jim Newall for their work in the preparation of this document.

Impact maths sample medium-term plans for mathematics

Planning with the Framework

[The text of this page is reproduced with permission from the Department for Education and Skills.]

The Framework for teaching mathematics: Years 7, 8 & 9 provides teachers with guidance on meeting the National Curriculum requirements for mathematics. It sets out yearly teaching programmes showing how objectives for teaching mathematics can be planned from Year 7 to Year 9. A key task in developing medium-term plans for Key Stage 3 mathematics is to identify the objectives for the units of work that are going to be taught. In doing this, schools may choose to start from their existing schemes of work, or alternatively, may find that these sample plans provide a useful starting point.

The sample plans are designed to continue the progression and expectations established in the yearly teaching programmes up to Year 6. They are based on the examples of planning charts in the Framework. There are many other ways to organise the mathematics curriculum in Key Stage 3. The planning charts indicate dependencies between topics but the order and content of the units can be adjusted.

Each sample plan identifies core objectives that define a minimum expectation for the majority of pupils in a particular year group. Plans for particular year groups are designed to show:

  • Progression in the teaching objectives for each strand of the curriculum;
  • Links between the teaching objectives, bringing together related ideas across the strands;
  • Opportunities to revisit topics during the year (the pitch of the second and subsequent units of a topic need careful adjusting in the light of teachers’ assessment of pupils’ progress);
  • How objectives for using and applying mathematics can be incorporated into units.

For each term, suggested objectives for oral and mental mathematics are also identified. Oral and mental work can both support the main teaching programme as well as providing a means of regularly revisiting important elements.

Many schools set pupils for mathematics. Teachers of higher sets may well base their pupils’ work on the programme for a later year group, while teachers of lower sets may need to draw on objectives in the teaching programmes from a previous year group. As always, the success of setting depends on teachers in the mathematics department being involved in careful monitoring, close teamwork and co-operative planning to make sure that expectations for all pupils are suitably high and that lower expectations are not justified simply because pupils are in a lower set.

There are some secondary schools where, at present, relatively few pupils attain level 5 or above at the end of Key Stage 3. Pupils may lack a secure understanding of some of the work they have been taught earlier. To begin with, these schools should look carefully at the programmes for Year 5 and Year 6 and draw suitable teaching objectives from them when they are planning work for Year 7, making corresponding adjustments for Years 8 and 9. A decision like this would need to be reviewed before the start of the next school year to allow for improving standards over time.

How the plans are set out

Teaching objectives for oral and mental activities are placed at the beginning of the plan for each term. Objectives for the main activities areset out in four main columns:

  • The first identifies the areas of mathematics studied in the unit and identifies links to the supplement of examples in the Framework.
  • The second identifies support objectives from previous yearly teaching programmes. These are linked to the core objectives for each unit.
  • The third column sets out the core objectives for the year group, the ones you would expect to focus on for the majority of pupils.
  • The fourth provides extension objectives, to stretch able pupils, drawn from the next year’s teaching programme. These are linked to the core objectives for the unit.

Impact maths sample medium-term plans for mathematicsPage 1

Key Stage 3 National Strategy

YEAR 8 PLANNING CHART

Autumn
36 hours / Number/algebra 1
Integers, powers and roots / SSM1
Sequences functions and graphs / Geometrical reasoning: lines,
6 hours / angles and shapes
Handling data 1 / Construction
Probability / Algebra 2 / 6 hours
6 hours /
Number 2
/ Equations and
FDPRP / formulae / SSM 2
6 hours / 6 hours / Measures and mensuration
6 hours
Spring
33 hours / Algebra 3
Number 3
/ Integers, powers and
Place value / roots / SSM 3
Calculations / Sequences, functions / Transformations
Calculator methods / and graphs / Geometrical reasoning:
FDPRP / 6 hours / lines, angles and shapes
Solving problems / 6 hours
9 hours / Algebra 4
Handling data 2 / Equations and formulae
Handling data / Graphs
6 hours / 6 hours
Summer
36 hours /
Number 4
Calculations / Algebra 5
Measures / Sequences, functions and
6 hours / graphs
Equations and formulae
Solving problems / 8 hours
Solving problems, / SSM 4
Handling data 3 / including FDPRP / Geometrical reasoning: lines, angles and shapes
Handling data, including / 6 hours / Transformations
probability / Mensuration
7 hours / 9 hours
35 weeks / 105 hours

Using and applying mathematics to solve problems should be integrated into each unit.

Impact maths sample medium-term plans for mathematicsPage 1

Key Stage 3 National StrategyYear 8: Autumn term

Numbers in the LH column refer to the supplement of examples for the core teaching programme

YEAR 8 – AUTUMN TERM

Teaching objectives for the oral and mental activities

2R / 2R
  • Order, add, subtract, multiply and divide integers.
  • Multiply and divide decimals by 10, 100, 1000.
  • Count on and back in steps of 0.4, 0.75, 3/4…
  • Round numbers, including to one or two decimal places.
  • Know and use squares, positive and negative square roots, cubes of numbers 1 to 5 and corresponding roots.
  • Convert between fractions, decimals and percentages.
  • Find fractions and percentages of quantities.
  • Know or derive complements of 0.1, 1, 10, 50, 100, 1000.
  • Add and subtract several small numbers or several multiples of 10, e.g. 250 + 120 – 190.
  • Use jottings to support addition and subtraction of whole numbers and decimals.
  • Calculate using knowledge of multiplication and division facts and place value, e.g. 432  0.01, 37  0.01.
  • Recall multiplication and division facts to 10  10.
  • Use factors to multiply and divide mentally, e.g. 22  0.02, 420  15.
/ 5.3 (pt), 8.1–8.4
5.3
3.5
3.1B, 6.2
5.3, 5.5
5.3, 5.5 /
  • Multiply and divide a two-digit number by a one-digit number.
  • Use partitioning to multiply, e.g. 13  1.4.
  • Use approximations to estimate the answers to calculations, e.g. 39  2.8.
  • Solve equations, e.g. 3a – 2 = 31.
  • Visualise, describe and sketch 2-D shapes.
  • Estimate and order acute, obtuse and reflex angles.
  • Use metric units (length, mass, capacity) and units of time for calculations.
  • Use metric units for estimation (length, mass, capacity).
  • Convert between m, cm and mm, km and m, kg and g, litres and ml, cm² and mm².
  • Discuss and interpret graphs.
  • Apply mental skills to solve simple problems.
/ 14.3, 14.5
7.3
12.1, 12.3, 12.6A&B, 12.7, 13.5

Teaching objectives for the main activities

Number/ Algebra1 (6 hours) / SUPPORT from the Y7 teaching programme / 2G / 2B / 2R / CORE from the Y8 teaching programme / 2G / 2B / 2R / EXTENSION from the Y9 teaching programme / 2R
Integers, powers and roots (48–59) /
  • Understand negative numbers as positions on a number line.
  • Order, add and subtract positive and negative integers in context.
/ 10.1, 10.3, 10.4, 10.7
10.2, 10.5
10.6
10.8
10.9 / 10.2
10.1, 10.3 10.4 / 8.2
8.1, 8.3 /
  • Add, subtract, multiply and divide integers.
/ 1.6, 1.8, 1.11–1.14, 3.1–3.4, 3.8– 3.11, 10.4–10.9 / 1.3, 1.8, 1.9, 3.1, 3.2, 3.7– 3.11, 10.4 / 8.3, 8.4, 8.5
  • Use tests of divisibility.
/ See notes / See notes / See notes /
  • Recognise and use multiples, factors (divisors), common factor, highest common factor, lowest common multiple and primes.
  • Find the prime factor decomposition of a number (e.g. 8000 = 2³ x5³).
/ 3.5, 3.6
See notes
– / 3.3–3.5
– / 1.2
– /
  • Use the prime factor decomposition of a number
/ –
  • Recognise the first few triangular numbers, squares of numbers to at least 12 x12 and the corresponding roots.
/ 3.7 / 3.6 / 1.3 /
  • Use squares, positive and negative square roots, cubes and cube roots, and index notation for small positive integer powers.
/ 3.6, 3.7 (in pt)
see notes / 3.6, 3.11 / 1.3 /
  • Use ICT to estimate square roots and cube roots.
  • Use index notation for integer powers and simple instances of the index laws.
  • Know and use the index laws in generalised form for multiplication and division of integer powers.
/ 18.1 (in pt)
10.2
10.3
Sequences and functions (144–157) /
  • Generate and describe integer sequences.
/ 5.1–5.4 / 5.1–5.4 / 9.1, 9.2, 9.4
  • Generate terms of a simple sequence, given a rule.
/ 5.4 / 5.4 / 9.4 /
  • Generate terms of a linear sequence using term-to-term and position-to-term definitions of the sequence, on paper and using a spreadsheet or graphical calculator.
/ 5.4, 17.2, 17.4 / 5.4, 17.3, 17.5 / 9.1–9.4, 18.3, 18.5
  • Generate sequences from practical contexts and describe the general term in simple cases.
/ 16.1 / 16.1 / 9.1, 9.4 /
  • Begin to use linear expressions to describe the nth term of an arithmetic sequence, justifying its form by referring to the activity or practical context from which it was generated.
/ – / 5.4 / 9.5
Notes (2G)
  • Tests of divisibility are covered in 1G.
  • HCF, LCM and prime factors are covered in 3G.
  • Cubes and index notation are covered in 3G.
/ Notes (2B)
  • Tests of divisibility are covered in 1G and 1R.
/ Notes (2R)
  • Tests of divisibility are covered in 1R.

Shape, space and measures1 (6 hours) / SUPPORT from the Y7 teaching programme / 2G / 2B / 2R / CORE from the Y8 teaching programme / 2G / 2B / 2R / EXTENSION from the Y9 teaching programme / 2R
Geometrical reasoning: lines, angles and shapes (178–189) /
  • Use correctly the vocabulary, notation and labelling conventions for lines, angles and shapes.
/ 2.9, 9.1–9.4 / 2.9
9.1–9.3 / 2.5, 7.1
  • Identify parallel and perpendicular lines.
  • Know the sum of angles at a point, on a straight line and in a triangle, and recognise vertically opposite angles.
  • Use angle measure.
  • Distinguishbetween and estimate the size of acute, obtuse and reflexangles.
/ 9.1
2.7, 2.8
2.2
2.3–2.6 / 9.1
2.7
2.8
2.2
2.3–2.6 / 2.10
2.4
2.1
2.2, 2.3 /
  • Identify alternate angles and corresponding angles.
  • Understand a proof that:
  • the sum of the angles of a triangle is 180º and of a quadrilateral is 360º
  • the exterior angle of a triangle is equal to the sum of the two interior opposite angles.
/ –
2.10 (in pt)
– / –
2.10
– / 2.10
2.6
2.7 /
  • Explain how to find, calculate and use:
  • the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons.
  • the interior and exterior angles of regular polygons.
/ 2.9
2.8
  • Solve geometrical problems using side and angle properties of equilateral, isosceles and right-angled triangles and special quadrilaterals, explaining reasoning with diagrams and text.
  • Classify quadrilaterals by their geometric properties.
/ 9.2 (in pt) see notes
9.2 / 9.1, 9.2
9.2 / 7.3
7.4 /
  • Solve problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons.
  • Know the definition of a circle and the names of its parts.
/ 2.10
7.1
Construction
(220–223) /
  • Use a ruler and protractor to:
  • measure and draw lines to the nearest millimetre and angles, including reflex angles, to the nearest degree.
  • construct a triangle given two sides and the included angle (SAS) or two angles and the included side (ASA).
/ 2.4, 2.5
– / 2.4, 2.5
– / 2.2, 2.3
– /
  • Use straight edge and compasses to construct:
  • the mid-point and perpendicular bisector of a line segment.
  • the bisector of an angle.
  • the perpendicular from a point to a line.
  • the perpendicular from a point on a line.
/ –
–
–
– / –
–
–
– / –
7.5
–
– /
  • Use straight edge and compasses to construct a triangle, given right angle, hypotenuse and side (RHS).
/ –
Solving problems
(14–17) /
  • Investigate in a range of contexts: shape and space.
/ 9.4 / 7.3
17J
Notes (2G)
  • Side and angle properties of triangles are not covered.
/ Notes (2B) / Notes (2R)
Handling data1 (6 hours) / SUPPORT from the Y7 teaching programme / 2G / 2B / 2R / CORE from the Y8 teaching programme / 2G / 2B / 2R / EXTENSION from the Y9 teaching programme / 2R
Probability
(276–283) /
  • Use the vocabulary of probability when interpreting the results of an experiment.
  • Appreciate that random processes are unpredictable.
/ 7.1–7.5
– / 7.1, 7.6
– / 4.1, 4.5
–
  • Understand and use the probability scale from 0 to 1.
  • Find and justify probabilities based on equally likely outcomes in simple contexts.
  • Identify all the possible mutually exclusive outcomes of a singe event.
/ 7.3
7.4
7.5, 7.6 / 7.1, 7.2
7.3, 7.4
7.4 / 4.1
4.2
4.2 /
  • Know that if the probability of an event occurring is p, then the probability of it not occurring is 1 – p.
  • Find and record all possible mutually exclusive outcomes for single events and two successive events in a systematic way, using diagrams and tables.
/ 7.4 (in pt) see notes
– / 7.5, 7.6
– / 4.3–4.5
4.6 /
  • Identify all the mutually exclusive outcomes of an experiment.
  • Know that the sum of probabilities of all mutually exclusive outcomes is 1 and use this when solving problems.
/ 4.5
4.6
  • Collect data from a simple experiment and record in a frequency table.
  • Estimate probabilities based on this data.
/ –
– / 7.6
7.6 / 7.5
7.5 /
  • Estimate probabilities from experimental data.
  • Understand that:
  • if an experiment is repeated there may be, and usually will be, different outcomes.
  • increasing the number of times an experiment is repeated generally leads to better estimates of probability.
/ see notes / 7.6
7.6
– / 4.5
4.5
4.5 /
  • Compare experimental and theoretical probabilities in a range of contexts.
  • Appreciate the difference between mathematical explanation and experimental evidence.
/ –
4.5
Notes (2G)
  • (1 – p) is covered in 3G.
/ Notes (2B) / Notes (2R)
Number 2 (6 hours) / SUPPORT from the Y7 teaching programme / 2G / 2B / 2R / CORE from the Y8 teaching programme / 2G / 2B / 2R / EXTENSION from the Y9 teaching programme / 2R
Fractions, decimals, percentages
(60 – 77) /
  • Use fraction notation to express a smaller whole number as a fraction of a larger one.
  • Simplify fractions by cancelling all common factors and identify equivalent fractions.
  • Convert terminating decimals to fractions.
/ 6.1
6.5
– / 6.1
6.2
– / 3.1
3.2
3.3
– /
  • Know that a recurring decimal is a fraction.
  • Use division to convert a fraction to a decimal.
  • Order fractions by writing them with a common denominator or by converting them to decimals.
/ –
8.8 (pt), 17.7
– / –
–
6.3 / 3.4
3.5, 5.6
5.6, 5.8
  • Add and subtract simple fractions and those with common denominators
  • Calculate fractions of quantities (whole-number answers).
  • Multiply a fraction by an integer.
/ 6.3, 6.6
6.4
– / 6.5
6.5
6.4 / 3.6
3.1
3.9 /
  • Add and subtract fractions by writing them with a common denominator
  • Calculate fractions of quantities (fraction answers)
  • Multiply and divide an integer by a fraction.
/ 6.6 (in pt)
–
– / 6.5
–
– / 3.6, 3.7
3.8
3.9 /
  • Use efficient methods to add, subtract, multiply and divide fractions, interpreting division as a multiplicative inverse.
  • Cancel common factors before multiplying or dividing.
/ 3.8
3.10
3.12
  • Understand percentage as the 'number of parts per 100'
  • Calculate simple percentages.
/ 8.8
8.9
17.3 / 8.9, 8.11
8.8 (pt), 8.9, 8.14 / –
6.2 /
  • Interpret percentage as the operator 'so many hundredths of' and express one given number as a percentage of another.
  • Use the equivalence of fractions, decimals and percentages to compare proportions.
  • Calculate percentages and find the outcome of a given percentage increase or decrease.
/ 8.7–8.9
8.8, 8.9
– / 8.9–8.12
8.14
8.13, 17.4 / 6.1, 6.2
6.4, 6.5
6.3 /
  • Solve problems involving percentage changes.
/ 6.7, 6.8
Calculations (82–85, 88–101) /
  • Understand addition and subtraction of fractions.
  • Use the laws of arithmetic and inverse operations.
/ 6.6 (in pt)
1.11–1.14, 5.2–5.4 / 6.5
1.3, 1.7–1.9, 3.1, 3.2, 3.7–3.11 / 3.6, 3.7
3.8–3.10
  • Consolidate the rapid recall of number facts, including positive integer complements to 100 and multiplication facts to 10 x10, and quickly derive associated division facts.
/ 3.1, 3.2, 3.4 (in pt) / 3.1, 3.2 / – /
  • Recall known facts, including fraction to decimal conversions.
  • Use known facts to derive unknown facts, including products involving numbers such as 0.7 and 6, and 0.03 and 8.
/ 1.5
1.12 / 1.7
1.7 / 5.5
5.5 /
  • Use known facts to derive unknown facts.
/ 5.5
  • Consolidate and extend mental methods of calculation, working with decimals, fractions and percentages.
  • Solve word problems mentally.
/ see notes / see notes / 5.1, 5.5 see notes /
  • Extend mental methods of calculation, working with factors, powers and roots.
/ –
Notes (2G)
  • Mental methods of calculation are covered by starters 1.3, 1.5, 1.7, 1.11, 1.12, 6.1, 6.2, 6.5, 8.1–8.3.
/ Notes (2B)
  • Mental methods of calculation are covered by starters 8.2 and 8.3.
/ Notes (2R)
  • Mental methods of calculation are covered by starters 5.1, 5.3–5.5.

Algebra2 (6 hours) / SUPPORT from the Y7 teaching programme / 2G / 2B / 2R / CORE from the Y8 teaching programme / 2G / 2B / 2R / EXTENSION from the Y9 teaching programme / 2R
Equations and formulae
(112-119, 138-143) /
  • Use letter symbols to represent unknown numbers or variables.
  • Know the meanings of the words term, expression and equation.
/ 4.1, 13.3
4.3, 13.6 / 13.2
4.1, 13.4 / 10.1
10.1 /
  • Begin to distinguish the different roles played by letter symbols in equations, formulae and functions.
  • Know the meanings of the words formula and function.
/ 4.1, 4.2
13.1 (pt) / Ch 4 start
13.1 (pt) / 10.1
14.1
  • Know that algebraic operations follow the same conventions and order as arithmetic operations.
  • Use index notation for small positive integer powers.
/ 4.1, 4.2, 4.5, 4.6, 13.4
3.11 (in pt) see notes / 4.2, 4.5
see notes / 10.4, 14.1
10.1, 10.2 /
  • Use index notation for integer powers and simple instances of the index laws.
/ 10.3
  • Simplify linear algebraic expressions by collecting like terms.
/ 4.2 / 4.1–4.3 / 10.1 /
  • Simplify or transform linear expressions by collecting like terms.
  • Multiply a single term over a bracket.
/ 4.3
4.4
– / 4.1
4.3
4.4 / 10.4, 14.6
10.5, 14.7 /
  • Simplify or transform algebraic expressions by taking out single-term common factors.
/ 10.6
10.7
  • Use formulae from mathematics and other subjects.
  • Substitute integers into simple formulae, and positive integers into expressions involving small powers (e.g. 3x² + 4 or 2x³).
  • Derive simple formulae.
/ 13.1
13.3–13.6, see notes
13.3 (pt) / 13.1
13.3–13.6
13.3 (pt) / 14.1
14.3
14.2
Notes (2G)
  • Index notation is covered in 3G.
  • Powers are covered in 3G.
/ Notes (2B)
  • Index notation is covered in 3B.
/ Notes (2R)
Shape, space and measures 2 (6 hours) / SUPPORT from the Y7 teaching programme / 2G / 2B / 2R / CORE from the Y8 teaching programme / 2G / 2B / 2R / EXTENSION from the Y9 teaching programme / 2R
Measures and mensuration (228-231, 234-241) /
  • Convert one metric unit to another (e.g. grams to kilograms).
  • Read and interpret scales on a range of measuring instruments.
/ 9.7
9.8
9.10
– / 9.8
9.9 / – /
  • Use units of measurement to estimate, calculate and solve problems in everyday contexts involving length, area, volume, capacity, mass, time and angle.
  • Know rough metric equivalents of imperial measures in daily use (feet, miles, pounds, pints, gallons).
/ 9.7, 9.8, 9.10
9.9 / 9.8, 9.9, 9.11
9.10 / see notes
7.10 /
  • Convert between area measures (mm² to cm², cm² to m², and vice versa) and between volume measures (mm³ to cm³, cm³ to m³, and vice versa).
/ 15.3 (in pt)
  • Know and use the formula for the area of a rectangle.
  • Calculate the perimeter and area of shapes made from rectangles.
/ 14.2
14.4 / 14.2
14.4 / – /
  • Deduce and use formulae for the area of a triangle, parallelogram and trapezium.
  • Calculate areas of compound shapes made from rectangles and triangles.
/ see notes / 14.3–14.5
14.1–14.5 / 15.1–15.3
15.2 /
  • Know and use the formulae for the circumference and area of a circle.
/ 15.4
  • Calculate the surface area of cubes and cuboids.
/ see notes / see notes / see notes /
  • Know and use the formula for the volume of a cuboid.
    Calculate volumes and surface areas of cuboids and shapes made from cuboids.
/ 14.6, 14.7
– / 14.10, 14.11
– / 15.5
see notes /
  • Calculate the surface area and volume of right prisms.
/ –
Solving Problems
(18–21) /
  • Investigate in a range of contexts: measures.
/ – / – / –
Notes (2G)
  • For area of a triangle etc., see starters 14.1 and 14.3.
  • Surface area of a cuboid is covered in 1G.
/ Notes (2B)
  • Surface area of a cuboid is covered in 1G and 1R.
/ Notes (2R)
  • Using units of measurement in everday contexts is covered in 1R.
  • Surface area of a cuboid is covered in 1R.

Impact maths sample medium-term plans for mathematicsPage 1

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